"It's weird. I used to live on the road just over there. I was always aware of this amazing building being here, but I never imagined I'd ever have a reason to enter it." Dressed in effortless indie attire - black Chelsea boots, skinny jeans and T-shirt - Mr Justin Young sits on a marble doorstep opposite the iconic Maida Vale recording studios. It's the release day of The Vaccines' second album, Come of Age and lazing in the early autumn sun is a front man with an attitude that's as punchy as his choruses. "We just want to be as big as we possibly can be. I just think, we're here now - I don't know what's going to happen next year, but tomorrow's going to be fun."

From posting raucous debut "If You Wanna" on YouTube in 2011, to a hit first album on Columbia Records (What Did You Expect From The Vaccines? became the biggest-selling debut by a band in the UK in 2011), and today's live sessions for BBC Radio 1 - the West Londoners have come a long way.

Their story of success is a familiar one. After Mr Young and guitarist Mr Freddie Cowan met on a summer's day in 2009 to experiment with some instruments, they simply "went on a roll". Critics and radio DJs heralded their first track, a debut London show in late 2010 sold out instantly, and they became darlings of the British music press, touted as leaders of a new wave of guitar music akin to New York rockers The Strokes.

We turned down magazine covers and interviews to try to slow it down. But at the end of the day it happened because people wanted to hear our music

In an increasingly fickle music industry, however, it felt premature. It seemed to be hype rather than substance. "We turned down magazine covers and interviews to try to slow it down," says Mr Young, earnestly. "We wanted to build a foundation. But at the end of the day it happened because people wanted to hear our music." Too right. In March 2011, less than two years after the band had formed, their first album shot to No.4 in the UK charts. No mean feat for an alternative guitar outfit still wet behind the ears.

So, how does Mr Young feel about the much-anticipated follow up? "I don't know. When I think back to 18 months ago and I think of the phases it went through - I can't imagine that happening again." Perhaps it was tactical modesty, but Mr Young needn't have been so cautious. In the week following the shoot, Come of Age has rocketed to No.1 in the UK album charts.

If their tongue-in-cheek debut What Did You Expect represented them riding that early hype, then their second attempts a level of maturity - proof they've settled into themselves and evolved. There's certainly more swagger second time around, and Mr Young agrees. "I think I was a bit wet on the first record. I think there's more attitude on this one... more confidence. The first one was heavily referential." Sticking to a formula of infectious melodies and pithy lyrics, Mr Freddie Cowan's lead guitar shows bravado on the likes of "I Always Knew", while Mr Young's vocals bark over tracks such as "Bad Mood".

The artwork for The Vaccines' second album Come of Age

Opener "No Hope", however (with the line "The whole thing feels like an exercise in trying to be someone I would rather not be") and latest single "Teenage Icon" - a gleeful list detailing Mr Young's inadequacy as a front man - question whether The Vaccines are more assured at all. "I'm in my mid-twenties now", says Mr Young when I quiz him. "You'd think at this point in your life you've worked out who you are, but I've found this period of my life harder and more confusing... It's kind of a searching record - about it being hard to come of age as people."

Personal disillusionment is understandable for a young front man in a whirlwind of tours, journalists and fans. As a group, however, The Vaccines seem more united than ever, and are looking to cement their future. What's in store beyond the coming tour? "We've got to try to find our place in rock's landscape and work out what it is we're about and what we can bring artistically. What's going to make people compare new bands to The Vaccines in 10 years? We want to be a popular band, too. We've all struggled for so long - and all of a sudden it clicked."

And how. As they prepare for tour dates in the US, Mexico and Europe, then Australia at Christmas and then Asia, The Vaccines are projecting their poppy brand of indie rock onto the international stage in style. And what's more, they're not afraid to enjoy it.